Very basic rules of thumb are to go for, in this order:
- 5-matches (duh) - but starting from the top so as to not ruin other ones
- 4-matches - if they are numerous, start from the top as above...
- ... but if not, try to hit lower on the board to potentially trigger 5-matches
- 3-matches - lower on the board as above
A major trick is getting used to the behavior of these things when they're matched, since unlike gems they will leave an object behind.
Other things to remember:
A main goal is to (counter-intuitively) avoid having all the 5-/4-matches trigger in one move because you won't net the benefit of the extra turns. Although the cascades do still increase your board's value.
Also try to prevent lower-value coins (especially red/bronze coins but also blue ones) from getting near the bottom. They become hard to match and clog the board up from there.
Be prepared to chance getting a blue coin, gold coin, or brown box coming down from the top if you match a vertical set - easy way to potentially net an unexpected 5-match if you've got nothing else going for you.
Don't match 4 or 5 green/red chests unless you really have to - its more valuable to keep them around and prevent them from being absorbed (weigh the extra/turn over the potential loot - it may be worth having 5 red chests and having the game end vs getting a few more turns by matching them into one vault).
Leave matching the red chests for opportune moments because the vaults can't be moved afterward (and can cause problems) - always attempt to get them on the bottom row.